Related papers: Left determined model structures for locally prese…
Let $\mathcal{S}$ be a small category, and suppose that we are given a full subcategory $\mathcal{U}$ such that every object of $\mathcal{S}$ can be embedded into some object of $\mathcal{U}$ in the same way as every quasi-projective…
We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact and semi-separated scheme X. The approach generalizes and simplifies methods used by the author to build monoidal…
In two papers we noted that in common practice many algebraic constructions are defined only `up to isomorphism' rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper…
We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations…
The hammock localization provides a model for a homotopy function complex in any Quillen model category. We prove that a homotopy between a pair of morphisms induces a homotopy between the maps induced by taking the hammock localization. We…
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…
In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…
Definability is a key notion in the theory of Grothendieck fibrations that characterises when an external property of objects can be accessed from within the internal logic of the base of a fibration. In this paper we consider a…
We prove that the 2-category Grt of Grothendieck abelian categories with colimit preserving functors and natural transformations is a bicategory of fractions in the sense of Pronk of the 2-category Site of linear sites with continuous…
We show that the theory of derivators (or, more generally, of fibered multiderivators) on all small categories is equivalent to this theory on partially ordered sets, in the following sense: Every derivator (more generally, every fibered…
We show that the model category of diagrams of spaces generated by a proper class of orbits is not cofibrantly generated. In particular the category of maps between spaces may be given a non-cofibrantly generated model structure.
The purpose of this note is to consider in detail the construction of derived functors. The classical construction, such as in Cartan-Eilenberg or Grothendieck, is clarified, and it is shown, at the same time, that everything can be…
It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…
We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring…
We show that the conditions in Steimle's 'additivity theorem for cobordism categories' can be weakened to only require \emph{locally} (co)Cartesian fibrations, making it applicable to a larger class of functors. As an application we compute…
Associated to each small category $C$, there is a category of $C$-shaped diagrams of simplicial sets and an $\infty$-category of $NC$-shaped homotopy coherent diagrams of spaces. We present a functor which exhibits the latter as the…
Localic and realizability toposes are two central classes of toposes in categorical logic, both arising through the Hyland-Johnstone-Pitts tripos-to-topos construction. We investigate their shared geometric features by providing an…
We give a proof of the existence of generalized definable locally compact models for arbitrary approximate subgroups via an application of topological dynamics in model theory. Our construction is simpler and shorter than the original one…
We define two-cocycles and cleft extensions in categories that are not necessarily braided, but where specific objects braid from one direction, like for a Hopf algebra $H$ a Yetter-Drinfeld module braids from the left with $H$-modules. We…